consider the following system of equations . y = 2x - 4 y = -x - 5

Consider the following system of equations.  y = 2x - 4 y = -x - 5

a. Identify the slope and y-intercept of the graph of each equation.

b. Based on your answer for part (a), are the graphs of the two lines intersecting lines, the same line, or parallel lines? Explain.

i-can

Page 92 of your INB

Write down this problem on yourREADY RECALL SHEET

Be prepared to explain your answer if you are called on.

find the solution by using the Elimination method:

-4x - 15y = -17 -x + 5y = -13

ITEMS of BUSINESS

Questions on Homework?then Trade-n-Grade

SYSTEMS OF EQUATIONS

11.3 Solving Systems by Elimination

i-canGet into your Groups

Page 92-93 of your INB

find the solution by using the Elimination Method:

-4x - 15y = -17 -x + 5y = -13

MATHICAL MAGGIE

Did you know I’m Magic?

I can read your mind

Think of 2 numbersTell me the Sum and Difference

MATHICAL MATT/MAGGIE

ARE YOUMAGICAL NOW?Show your Partner

Think of 2 numbersTell them the Sum and Difference

How is it done Algebraically?

For any x or yx + y = SUM

x – y = DIFFERENCE

SUM  +  DIFFERENCE2 = x

SUM – x = yEx. x + y = 30 x – y = 6

30 + 62 = 18 30 – 18 = 12 x = 18

y = 12I’M USING THE ELIMINATION METHOD!!

x + y = 30x – y = 6 ADD THE TWO

EQUATIONS TOGETHER & SOLVE

2x = 362 2x = 18

REPLACE x WITH 18IN ONE OF THE ORIGINAL

EQUATIONS & SOLVE FOR Y

18 + y = 30y = 30 - 18y = 12

x = 18, y = 12 (18,12)

Open your Books

to page 648.

ELIMINATION METHODPG. 648

ELIMINATION METHODPG. 648

ELIMINATION METHOD PG. 649

x = 179 girls; y = 145 boys

LETS TRY A PROBLEM

1. x - y = 11 2x + y = 19

Front Page of your homework: A. Guided Practice

IS THIS TRUE?If we

have… y = 4

2(y) = 2(4)2y =

8y = 4

Multiply each side by 2, will it still be true?

3(y) = 3(4)3y = 12y = 4

Multiply each side by 3, will it still be true?

-1(y) = -1(4)-1y = -

4y = 4

Multiply each side by -1, or oppositize both sides. Will it still be true? Sooo…

Is each equation still

true if we Multiply each side with a

Scaleror Oppositize

them?

LETS PRACTICE WITH OUR COMMUNICATORS

Example: Multiply both sides with 3 x + 2y = 7 3x + 6y = 21

A. Multiply both sides with 2 3x - y = 4 6x - 2y = 8B. Multiply both sides with -4 x - 4y = 2 -4x + 16y = -8

C. Oppositize both sides x - 3y = -5 -x + 3y = 5

What would you do to prepare these equations for

elimination?

𝐴 .3 𝑥+3 𝑦=−213 𝑥−2 𝑦=14

B.

C .−4 𝑥+9 𝑦=9𝑥−3 𝑦=−6

ELIMINATIONWhen using Elimination, we might need to use a

Scaler or to Oppositize in order to eliminate a variable. Front Page of your homework: A. Guided Practice

2. 7x + 2y = 24 8x + 2y = 30

A. Solve by Elimination:{ 5x + 2y = 12

-5x + 4y = -66+ 6y = -54 6 6y = -9

5x + 2y = 12 5x + 2(-9) = 12

5x - 18 = 12+18 +18

5x = 305 5

x = 6

INB

NOTE

BOOK

AC

TIVI

TY

Solution: (6, -9)

x, y

B. Solve by Elimination:

– 15y

{ 3x – 5y = -6 -9x + 15y = 13

9x-9x + 15y = 13+

0 = -5Is this true?

( ) 3

= -18

No!INB

NOTE

BOOK

AC

TIVI

TY

NO SOLUTION

C. Solve by Elimination:

Is this true?Yes!

– 12y

{ 2x – 4y = 6

-3x + 6y = -9 6x -6x+

0 = 0

( )3

= 18

( )2

+ 12y = -18

INB

NOTE

BOOK

AC

TIVI

TY

Infinite Solutions

POSSIBLE SOLUTIONS FOR 2 EQUATIONS

One Solution No SolutionInfinitely

Many Solutions

(1,3)

Intersecting LinesSame Slope, y-int. can be

different or the same

Solve Algebraically: You will get one solution

(X,Y)

Parallel LinesSame slope, different y-int.  

Solve Algebraically: Variables drop out FALSE Statement

ex. 12 = 9

Coincidental LinesSame line, same slope, same y-int.

Solve Algebraically: Variables drop out TRUE Statement

ex. 22 = 22

INB NOTEBOOK ACTIVITY

ONE SOLUTION: (X,Y) ONE SOLUTION: (X,Y)

FALSE STATEMENT FALSE STATEMENT

TRUE STATEMENT TRUE STATEMENT

LETS TRY A FEW PROBLEMS

1. 2x - y = 5 2x – y = 7

Second Page of your homework: B. Guided Practice

2. 2x – y = 3 4x - 2y = 6

i-can find the solution byusing the Elimination method:

Number 14 on your Homework

11.3 Solving Systems by Elimination

-4x - 15y = -17 -x + 5y = -13

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11.3 Solving Systemsby Elimination